Are there real applications of fuzzy logic?
You've obviously never heard of fuzzy logic washing machines.


  ● Typically, fuzzy logic controls the washing process, water intake,water temperature, wash time, rinse performance, and spin speed. This optimises the life span of the washing machine. More sophisticated machines weigh the load (so you can’t overload the washing machine), advise on the required amount of detergent, assess cloth material type and water hardness, and check whether the detergent is in powder or liquid form. Some machines even learn from past experience,memorising programs and adjusting them to minimise running costs. 


Fuzzy logic is used in a variety of control applications.  If your furnace can only be on or off, for example, you might use a probabilistic function of temperature to determine when to turn it on and off, rather than having fixed high and low temperatures activate your thermostat.  In some applications, that's been found to improve perceived comfort or efficiency.

For more sophisticated AI applications, you could use fuzzy logic for activations in a neural net, but I don't think it's offering much improvement over fixed, weighted activations.